arXiv subjects

Ashok Gopalarathnam

Publications and source records attributed to Ashok Gopalarathnam.

3 recordsLinked to original sources

arXiv2026

Physically consistent formulation for the bound vortex sheet strength in the Wagner model

Unsteady thin-airfoil theory (UTAT) coupled with discrete-vortex methods has been widely employed in reduced-order aerodynamic modeling. Due to the non-uniqueness of potential-flow solutions, the Kutta condition is imposed to determine the circulation around the airfoil. Although the unsteady Kutta condition is commonly associated with the zero-loading condition at the trailing edge, its implications for the continuity of the vortex-sheet strength remain comparatively underexplored. In particular, the classical series expansion employed for the bound vorticity in unsteady thin-airfoil theory is not uniformly convergent at the trailing edge, leading to mathematical inconsistencies in the vortex-sheet and pressure distributions. In this context, the present work seeks to advance the mathematical framework of unsteady thin-airfoil theory through a physically consistent formulation of the bound vortex-sheet strength for the Wagner problem. A recurrence relation is derived for the Wagner coefficients, allowing the construction of a uniformly convergent series expansion for the bound vorticity. The proposed formulation ensures continuity between the bound and wake vortex sheets while simultaneously recovering zero pressure loading at the trailing edge, thereby providing a mathematically consistent representation of the unsteady Kutta condition. To investigate the implications of the modified framework, a discrete-vortex method based on UTAT is developed and compared with the classical formulation. The results demonstrate that the proposed approach eliminates spurious oscillatory behavior near the trailing edge and significantly improves the regularity of the computed vorticity and pressure distributions.

physics.flu-dyn↗

arXiv2025

Discrete vortex-based broadcast mode analysis for mitigation of dynamic stall

We integrate a discrete vortex method with complex network analysis to strategize dynamic stall mitigation over a pitching airfoil with active flow control. The objective is to inform actuator placement and timing to introduce control inputs during the transient evolution of dynamic stall. To this end, we represent the massively separated flow as a network of discrete vortical elements and quantify the interactions among these vortical nodes by tracking the spread of displacement perturbations between each pair of elements using the discrete vortex method. This enables a network broadcast mode analysis to identify an optimal set of vortices, critical timing, and direction to seed perturbations as control inputs. Motivated by the goal of mitigating dynamic stall, the optimality is defined as minimizing the total circulation of free vortices generated from the leading edge over a prescribed time horizon. We demonstrate the framework on two cases: two-dimensional flow over a flat plate airfoil and three-dimensional turbulent flow over a SD7003 airfoil. The analysis reveals that optimal timing for introducing disturbances occurs just after separation onset, when the shear layer pinches up to form the core of the dynamic stall vortex. Broadcast modes indicate that vortical nodes along the shear layer are optimal for control, guiding actuator placement. Flow simulations validate these insights: placing actuators near the leading edge and triggering them shortly after separation yields a 12% and 30% reduction in peak lift for the flat plate and SD7003 cases, respectively. A corresponding decrease in vorticity injection under control confirms the analysis objective. This study highlights the potential of combining discrete vortex methods with network analysis to guide active flow control in unsteady aerodynamics.

physics.flu-dyn↗

arXiv2020

A Low-Order Method for Prediction of Separation and Stall on Unswept Wings

A low-order method is presented for aerodynamic prediction of wings operating at near-stall and post-stall flight conditions. The method is intended for use in design, modeling, and simulation. In this method, the flow separation due to stall is modeled in a vortex-lattice framework as an effective reduction in the camber, or "decambering." For each section of the wing, a parabolic decambering flap, hinged at the separation location of the section, is calculated through iteration to ensure that the lift and moment coefficients of the section match with the values from the two-dimensional viscous input curves for the effective angle of attack of the section. As an improvement from earlier low-order methods, this method also predicts the separation pattern on the wing. Results from the method, presented for unswept wings having various airfoils, aspect ratios, taper ratios, and small, quasi-steady roll rates, are shown to agree well with experimental results in the literature, and computational solutions obtained as part of the current work.

physics.flu-dyn↗